Not quite as awful as Izzie, but pretty horrible anyway. Very immature, in fact, flat out infantile. I'm not big on Bella or Belle either, in fact, I think the nicest nickname for an Isabella or Isabelle would be Isa.
Sounds like a little kid trying to say izzy. I don't think anyone would take someone named Isabel/Isabelle seriously if she decided to go by "ibbie". Izzy is equally childish and informal, why not just go by Isabel/Isabelle? It's such a pretty name on its own, who needs a nickname?